Computer Science > Distributed, Parallel, and Cluster Computing

Title:Multidimensional Asymptotic Consensus in Dynamic Networks

Abstract: We study the problem of asymptotic consensus as it occurs in a wide range of
applications in both man-made and natural systems. In particular, we study
systems with directed communication graphs that may change over time.
We recently proposed a new family of convex combination algorithms in
dimension one whose weights depend on the received values and not only on the
communication topology. Here, we extend this approach to arbitrarily high
dimensions by introducing two new algorithms: the ExtremePoint and the Centroid
algorithm. Contrary to classical convex combination algorithms, both have
component-wise contraction rates that are constant in the number of agents.
Paired with a speed-up technique for convex combination algorithms, we get a
convergence time linear in the number of agents, which is optimal.
Besides their respective contraction rates, the two algorithms differ in the
fact that the Centroid algorithm's update rule is independent of any coordinate
system while the ExtremePoint algorithm implicitly assumes a common agreed-upon
coordinate system among agents. The latter assumption may be realistic in some
man-made multi-agent systems but is highly questionable in systems designed for
the modelization of natural phenomena.
Finally we prove that our new algorithms also achieve asymptotic consensus
under very weak connectivity assumptions, provided that agent interactions are
bidirectional.

Subjects:

Distributed, Parallel, and Cluster Computing (cs.DC); Systems and Control (cs.SY)